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A few games that have a similar sort of thing: Citadels (players choose roles at the start of each round, and roles have a fixed turn order), El Grande (each round starts with bidding, where bids determine turn order), Mice and Mystics (turn order is randomized and laid out as a queue. Some abilities/monsters can modify the queue)
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bengoesboomNov 6 '13 at 16:47

7 Answers
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No matter what method you decide on, you will need to keep track of two things, the current turn order and the next turn order. I have a few options you could try:

Two Tracks

You can simply have two tracks that will show current and next turn orders. This is a simple solution, players can all stay in their seats and the turn will just jump around the table, this is good for certain games where the "player to your left" or "player to your right" kind of abilities do not exist.

Musical Chairs and Chips

This is good for games where "player to your left" or "player to your right" kind of abilities do exist. You have the players sit clockwise in turn order. And they will start each round holding a chip with their number on it. When switching turn orders throughout the game, players just switch these chips. At the start of each round, players will reseat themselves according to turn order.

Infinite Stacking Track

This is a bit complex, but the idea is that each player has a token with his color/team on it. And there is an "infinite" track, (this could just be a very long track) Initial turn order is decided and tokens are placed in that order on the track, whenever a player modifies a turn order, you simply move the token up or down the track, if a token already exists on that you place yours below that token.

This way, when a new turn is started, going from the first tile in the track towards the end and working from the top-most token down. You get an extra little mechanic where some tiles are blank, which means players after those tiles would need to work extra-hard to get ahead of those that are already passed them. The difference a regular track is that in a regular track you would just replace the tokens instead of stack them.

Double Secret Cards

This is a good method if at some point the turn order might be randomized, or you want to keep the turn order secret, similar to the Two Tracks suggestion you would have 2 sets of cards, one for the current turn, one for the next turn (maybe a different color on the back?) Players would start the game where both cards are the same number (turn order) and only when it's that players turn, he would reveal that he is the player with that number, (revealing the current card color) in this way, players can manipulate the turn order in secret (which adds an interesting element to the game).

The only pitfall is that players need to remember who they gave the next turn cards to, so they can also give them the current turn cards at the end of the turn.

You could do this with a board that has two columns, one for the current turn and one for the next turn. Place coloured counters on the board to show the turn order, move the counters when the turn order changes.

For your example if Jim is Red, Steve is Green and Betty is Blue, then start with this:

Current Next
1 Red Red
2 Green Green
3 Blue Blue

During round 1 Jim falls back, so swap the Red and Green counters in the Next column:

Current Next
1 Red Green
2 Green Red
3 Blue Blue

At the end of round one, remove all the counters from the Current column, move all the counters from the Next column into the Current column and place counters in the Next column to match the new Current column.

It seems like you would want a track showing the current turn order. The game boards for Kingsburg, Macao, and Powergrid all use a track like this. While Kingsburg and Powergrid determine turn order at the start of each round, Macao is more similar to what you describe; players can change their turn order during their turn.

Just have the action that players take allow them to move either up or down the turn track. You can either do exactly like Macao, and allow a player to stack on top of another player on the turn track (and whoever is on top goes first), or make it so that when you move up on the turn track, you swap positions with the person above you, so you never have 2 people on the same spot.

In terms of knowing whose turn it is next right after your turn, as long as you don't have the ability to change 2 other players' orders relative to each other, there shouldn't be an issue. At the end of your turn, you see who is the highest person on the turn track that hasn't already had a turn this round. Even if you moved up or down; that won't change; the next person who should go is whoever is highest on the track.

If turns are really long or complex, such that you are concerned with players knowing for sure who has or hasn't had a turn this round yet, you could have players flip their marker over at the end of their turn (and the other side of the market is different). Usually when we play Power Grid, after a player has obtained a plant during the auction, we'll move their marker up off the turn track to note that they are now out of the auction phase.

Changing players' turn orders relative to each other is the whole point, actually (see the example I gave with Jim, Steve, and Betty).
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JoeNov 7 '13 at 0:46

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@Joe, That's what I thought. In which case you don't need to worry about changing the track during the turn; you can still know whose turn is next based on who is highest on the track (that hasn't already had their turn).
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GendoIkariNov 7 '13 at 17:51

If you have player tokens/counters already in the game you could track turns with a single set and the dual track method mentioned above (trying to introduce fewer new components).
Basically track one is 'current turn' order, track two is 'next turn' order. The first player is the one with their token in the highest position of the 'current turn' track. When their turn is complete they move their token to the first open space in the 'next turn' track. An exception would occur if the first player did a 'push down' maneuver (they would then place their token in slot two). The player with the next highest token on the 'current turn' track then plays. When they are done they move their token to the 'next turn' track, on the first open spot - in this case slot 1 since player one did a 'push down'. If player two also did a 'push down' it would essentially negate player ones' 'push down' since they would be moving to slot 2 and player one would be moved back up to slot 1. When the last player has finished the only thing left to do is slide the tokens back to the turn track.

If your game is played only with cards then I would suggest two (or more) turn order sets.
Similar to what we have above, each player has a turn card from set one. When player ones' turn is over they draw the top card from set two (unless they played a 'push down' in which case they take the second) and turn in their set one turn card. The turn sets may need to be different colors to more easily keep track. Also, when drawing a set two card you may need to place it sideways (or something) to show that it's not in play yet. At the end of the last players turn, all of the set one cards have been turned in. Put them in order to draw from next. Set two cards should be placed upright and play proceeds with player one.

There have been a bunch of good comments. I hope you are able to find something helpful among these posts.

Each player can have a double sided token, with one side grayed out indicating that their turn has been taken.

These tokens can be placed on a track that indicates turn order. Once they start their turn, they flip the token to the grayed out side. If they take any actions that change their next turn order, simply move the token up or down the track as appropriate. Play then moves to the next unflipped token.

At the beginning of a new round, all tokens are flipped back to their coloured side.

This is what I was coming here to suggest. (That or dual tracks, but this seems more elegant to me.) I feel like I've seen this mechanic but I cannot remember in what game.
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Monica CellioFeb 3 '14 at 21:28

One solution would be to create a "track of tracks". To speak somewhat more formally, one could utilize an analogy to a permutation matrix.

Two kinds of objects are necessary for this:

A "ruler" marked "1st, 2nd, 3rd," etc. for each player, with sliding markers on them, which can be slid along the length of the ruler to indicate in which position that player is.

A square board, at least long enough to accommodate the number of players; it should be labeled with a grid, with cells labeled "1st, 2nd, 3rd," etc. sequentially as one descends a column, and identical through the rows.

Then let me work through its mechanism as through the example. At the beginning of the game, the initial order would be set by setting each player's ruler to their order, and then placing it (vertically) over the column of that order.

During the game, the names in the columns (in sequence) will correspond to the current turn's order, and the rows will correspond to the next turn's order. Thus, when Jim falls back one step, he indicates this by sliding his marker down one place on his ruler, and Steve's marker on his ruler up one:

And the order is Steve, Jim, Betty, etc. and so continues the example; each player takes their turns in order from left to right, tracks order changes by sliding the markers on the rulers accordingly, and at the end of each round, the rulers are rearranged back into a diagonalized order across the grid.

Many games with such systems have plates/tiles with marked turn orders that are passed out to players each turn and sit next to them on the table. It's much like the concept of a Dealer Button in poker, except that there's one for every position in the ordering. This can be seen in games such as Risk 2210 and Scepter of Zavandor. As a benefit, special rules relating to turn order can also be conveniently placed on the tiles - for example, in Zavandor, players in certain positions get higher or lower prices as a form of anti-feedback loop, and the order plates serve as a friendly reminder.